The first invention relates to a diffraction lens (also referred to as xe2x80x9clens with grating elementxe2x80x9d or xe2x80x9clens with diffraction elementxe2x80x9d in the following), in particular to a calculation (simulation) technique for calculating a diffraction efficiency of a diffraction lens that is cut with a diamond bit or molded using a die that is cut with a diamond bit, and a design technique for designing achromatic lenses.
Furthermore, the first invention relates to a lens with a grating element, particularly to a small size imaging apparatus such as a board camera or a monitoring camera etc. and a reading apparatus such as a bar code reader etc.
The second invention relates to an optical system for reading in which chromatic aberration is excellently corrected, and to an image reading apparatus and a bar code reader using the same.
In an optical system for imaging or an optical system for reading, imaging performance is of great importance. As factors that influence the imaging performance, there are those inside the optical system such as aberration of lenses, diffraction and dust, and those outside the optical system such as environmental conditions. Particularly, chromatic aberration due to different refractive indices of a lens at different wavelengths is one cause of deteriorating imaging performance.
Accordingly, conventional techniques try to reduce the chromatic aberration by combining several lenses having different Abbe numbers, and among other technologies, it is known that an anomalous dispersion glass may be used as an achromatic lens system.
Also, recently, as another technology for reducing chromatic aberration, a lens with diffraction element where a relief for providing diffractive effect is formed on a surface of the lens to correct chromatic aberration has been proposed. For example, in Publication of Unexamined Japanese Patent Application (Tokuhyo) No. Hei 8-508116, it is proposed to correct chromatic aberration in the entire visible spectrum by a single lens with diffraction element.
Recently, a large number of achromatic lenses and dual-focus lenses have been proposed where lens functionality is enhanced with diffraction lenses (see e.g. Publication of Unexamined Japanese Patent Application No. Hei 8-171052 and Japanese Patent Application No. Hei 8-290080). Most of these diffraction lenses are so-called relief-type diffraction lenses having a periodic relief on a surface of a lens or flat plate of, for example, glass.
There are basically two methods for forming a relief-type diffraction lens. One method is to cut the lens with a diamond bit. In this case, a saw-tooth-shaped relief (relief profile) can be cut. The other method involves photolithography and approximates this saw-tooth-shaped relief with a step relief. This is also called xe2x80x9cbinary methodxe2x80x9d.
Diffraction efficiencies are important parameters for the utilization and the design of diffraction lenses.
It is widely known, that according to Swanson et al (G. J. Swanson and Wilfrid B. Veldkamp, xe2x80x9cDiffractive optical elements for use in infrared systemsxe2x80x9d, Optical Engineering, Vol. 28, No. 6, (1989)), the relation between the number of masks used during manufacturing and the diffraction efficiency can be calculated for the binary method.
The retardation of the wave front passing a periodic relief-type diffraction grating with a grating ring interval (pitch) that is sufficiently longer than the wavelength and a phase shift of about one wavelength can be calculated from the refractive index of the grating material on the basis of its cross-section. It is widely known (see e.g. M. C. Hutley, xe2x80x9cDiffraction Gratingxe2x80x9d, Academic Press, Chap. 2, 1982) that when the retardation is Fourier-transformed, the diffraction efficiency of the diffraction grating can then be obtained as the Fourier coefficients (scalar diffraction theory).
FIG. 49(a) outlines how a die for the diffraction lens is cut with a diamond bit. A die 1901, which rotates in the arrow direction, is cut by a diamond bit 1902. The diamond bit has a pointed tip, which is suitable for cutting diffraction lenses or dies for diffraction lenses.
FIG. 49(b) is a magnification of FIG. 49(a) showing a cutting region A. The tip 1903 of the diamond bit describes a circular arc with a certain curvature radius (nose radius) 1904. Even when the designed shape is a saw-tooth shape as indicated by the chain double-dashed line 1905, the dent left by the diamond bit is a circular arc 1906 that has almost the same radius as the curvature radius of its tip.
FIG. 50 shows cross-sections outlining how a diffraction lens and a die are cut. For the sake of simplicity, the diffraction lens is formed on a planar substrate.
When the designed shape of the lens is as shown in FIG. 50(a), the designed shape of the die for manufacturing the lens is as shown in FIG. 50(b). However, when the die is cut with a diamond bit 2001 whose tip is a circular arch with a certain curvature radius, the convex angular portions in the cross-section of the die will be rounded out, as shown in FIG. 50(c). As a result, lenses that are formed with that die have a relief profile as shown in FIG. 50(d).
FIG. 50(e) is a magnification of the cross-section shown in FIG. 50(c), showing the microscopic features of the cutting region A after the cutting. Depending on the feed speed and the curvature radius of the cutting bit, cutting traces 2002 amounting to a tiny undulation remain on the cut surface. These cutting traces are transferred to the lens surface.
Since the diffraction efficiency of the diffraction lens is influenced by the relief profile, it may turn out to be quite different from the designed value, if the relief profile degenerates like this during the manufacturing step.
As mentioned above, the cutting bit can have a pointed tip to avoid a change of the diffraction efficiency, but then, many technically difficult problems arise. For example, the necessary cutting distance becomes long, the degeneration due to abrasion of the cutting bit becomes large, and the cutting bit chips more easily. As a result, the productivity becomes considerably worse.
If the relationship between the curvature radius of the cutting bit and the diffraction efficiency of the obtained diffraction lens were known, it could be decided before the cutting process which cutting bit should be chosen to keep the decrease in diffraction efficiency during the manufacturing process in a tolerable range, and the used bit would not have to be sharper than necessary, which would be very useful for the production efficiency.
If, at the design stage, the diffraction efficiency of the lens could be calculated with consideration to the processing method, then the processing method could be taken into account as one of the lens design parameters and lenses that are easier to manufacture could be designed. Consequently, there is a need for an easy calculation method for calculating, at the design stage, the finally attained diffraction efficiency with consideration to the processing method.
A typical example of an application for a diffraction lens is the use as an achromatic lens to correct the chromatic aberration of a refractive lens with the chromatic aberration of the diffraction lens. Such lenses are known, for example from Publications of Unexamined Japanese Patent Publication No. Hei 6-242373 and No. Hei 8-171052. In the lenses disclosed in both of these publications, the number of grating rings is large, so that it is difficult to cut a die for the lens using, for example, a diamond bit. Moreover, the diffraction efficiency can decrease due to deterioration of the shape because of the curvature at the vertex of the cutting bit. In the above publications, these problems were not addressed by the design considerations, so that it was difficult to ensure both diffraction efficiency and productivity.
Furthermore, in the above-mentioned conventional technologies, the pitches of the relief rings that form a grating element gradually decrease with increasing distance from the optical axis. Thus, the pitch becomes very small at the peripheral portion, so that problems such as decreased diffraction efficiency or processing difficulties may result.
Also, if lateral chromatic aberration (magnification chromatic aberration) of a wide-angle lens having a half field angle of at least 60xc2x0 is to be corrected with a single grating element surface, the focal length of the grating element must be short. However, in such a condition, longitudinal chromatic aberration (axial chromatic aberration) is excessively corrected, so that good imaging performance cannot be obtained. Furthermore, because the number of the relief rings also increases, problems such as decrease in diffraction efficiency or difficulty in processing may be caused.
Various optical systems for reading that form images from image information, or manuscript or code information etc. on an image sensor such as a charge-coupled device (CCD) have been proposed. It is required that such optical systems for reading should have modulation transfer function (MTF) that is high enough to project a manuscript on a CCD line sensor having high density, so that satisfactory correction of various aberrations is needed.
Conventionally, particularly in order to correct chromatic aberration as a cause of deterioration in imaging performance, combinations of multiple lenses with different Abbe numbers have been used. For example, in Publication of Unexamined Japanese Patent Application (Tokukai) No. Hei 5-119255, a technology that intends to correct chromatic aberration by forming an optical system for reading using three lenses in three groups, and also to enable low-cost production by using plastic materials as a lens material is disclosed. Furthermore, in Publication of Unexamined Japanese Patent Application (Tokukai) No. Hei 5-135193, a bar code reader, in which the optical system for reading is formed by using a single aspheric lens, is disclosed.
However, in the optical system for reading as disclosed in the above-mentioned Publication of Unexamined Japanese Patent Application (Tokukai) No. Hei 5-119255, due to the need for multiple lenses, low-cost production is limited in view of processing and assembly of the lenses. Furthermore, although it is intended to achieve low-cost production by using plastic materials for the lens materials, because types of plastic materials are limited, correction of chromatic aberration is also restricted. Also, in the bar code reader disclosed in the above-mentioned Publication of Unexamined Japanese Patent Application (Tokukai) No. Hei 5-135193, because chromatic aberration cannot be corrected and a single wavelength is required, a light source such as an LED is needed, thus limiting miniaturization and low-cost production.
To solve the above problems, it is an object of the first present invention to provide a simple method for calculating the diffraction efficiency of a lens molded with a die that was cut with a diamond bit.
It is another object of the first present invention to provide a combined refraction/diffraction lens that can be cut with high productivity using a diamond bit and which provides sufficient achromatism.
Furthermore, an object of the first invention is to solve the above-mentioned problems, and to provide a lens with a diffraction element that can be processed easily while utilizing the characteristics of conventional lenses with diffraction elements by devising the pitches of the relief rings which provide diffractive effect.
An object of the second invention is to solve the above-mentioned problems in conventional technologies, and provide an optical system for reading in which chromatic aberration is corrected without increasing the number of lens components and by which good imaging performance can be attained, and an image reading apparatus and a bar code reader using the same, by providing a surface of the lens with diffractive effect.
In accordance with a first configuration of the present invention, a device for calculating diffraction efficiencies of a diffraction lens divided into a plurality of regions, each region comprising at least one grating ring, comprises:
a first memory for storing information about diffraction efficiencies of the regions;
a second memory for storing information about weights corresponding to the regions;
a first processor for retrieving information from the first and the second memory, and calculating diffraction efficiencies of the entire diffraction lens in accordance with the formula                               E          j                =                              ∑                          m              =              1                        M                    ⁢                                    W              m                        ⁢                          η              mj                                                          (        1        )            
xe2x80x83wherein:
j: integer indicating the order of diffraction light
Ej: diffraction efficiency for j-th order diffraction light of the diffraction lens
M: positive integer (M greater than 1) indicating the number of regions for which the diffraction efficiency is calculated
m: index of the region for which the diffraction efficiency is calculated
xcex7mj: diffraction efficiency for the j-th order diffraction light of the m-th region (stored in the first memory)
Wm: weight for the m-th region (stored in the second memory means).
In accordance with the first configuration of the present invention, a method for calculating diffraction efficiencies of a diffraction lens divided into a plurality of regions, each region comprising at least one grating ring, comprises:
a first memory step of storing information about diffraction efficiencies of the regions;
a second memory step of storing information about weights corresponding to the regions;
a first processing step of retrieving information stored in the first and the second memory step, and calculating diffraction efficiencies of the entire diffraction lens in accordance with the formula                               E          j                =                              ∑                          m              =              1                        M                    ⁢                                    W              m                        ⁢                          η              mj                                                          (        1        )            
xe2x80x83wherein:
j: integer indicating the order of diffraction light
Ej: diffraction efficiency for j-th order diffraction light of the diffraction lens
M: positive integer (M greater than 1) indicating the number of regions for which the diffraction efficiency is calculated
m : index of the region for which the diffraction efficiency is calculated
xcex7mj: diffraction efficiency for the j-th order diffraction light of the m-th region (stored in the first memory step)
Wm: weight for the m-th region (stored in the second memory step).
In accordance with the first configuration of the present invention, a computer-readable recording medium stores a computer-executable program for calculating diffraction efficiencies of a diffraction lens divided into a plurality of regions, each region comprising at least one grating ring, which program executes:
a first memory step of storing information about diffraction efficiencies of the regions;
a second memory step of storing information about weights corresponding to the regions; and
a first processing step of retrieving information stored in the first and the second memory step, and calculating diffraction efficiencies of the entire diffraction lens in accordance with the formula                               E          j                =                              ∑                          m              =              1                        M                    ⁢                                    W              m                        ⁢                          η              mj                                                          (        1        )            
xe2x80x83wherein:
j: integer indicating the order of diffraction light
Ej: diffraction efficiency for j-th order diffraction light of the diffraction lens
M: positive integer (M greater than 1) indicating the number of regions for which the diffraction efficiency is calculated
m: index of the region for which the diffraction efficiency is calculated
xcex7mj: diffraction efficiency for the j-th order diffraction light of the m-th region (stored in the first memory step)
Wm: weight for the m-th region (stored in the second memory step).
In accordance with this first configuration of the present invention, the diffraction lens is divided into a plurality of regions, and a weight is assigned to each region to determine the diffraction efficiency of the entire lens, so that the diffraction efficiency of the entire lens can be calculated precisely and efficiently, even when the regions have different diffraction efficiencies. It is preferable that the calculation of diffraction efficiencies according to the present invention is performed on a computer.
In accordance with a second configuration of the present invention, a device for calculating diffraction efficiencies of a diffraction lens divided into a plurality of regions, each region comprising at least one grating ring, the diffraction efficiencies corresponding to a plurality of wavelengths, comprises:
a first memory for storing information about diffraction efficiencies of the regions at the plurality of wavelengths;
a second memory for storing information about weights corresponding to the regions;
a third memory for storing information about a relief cross-section shape of the diffraction lens;
a fourth memory for storing information about the plurality of wavelengths;
a fifth memory for storing information about refractive indices of a material of the diffraction lens at the wavelengths;
a fourth processor for calculating a relief cross-section shape of the diffraction lens stored in the third memory;
a second processor for retrieving information from the third, fourth and fifth memory, and calculating therefrom diffraction efficiencies of the regions at the plurality of wavelengths stored in the first memory;
a third repeating means for operating the second processor for a number of times that is equal to the number of the wavelengths;
a fourth repeating means for operating the third repeating means for a number of times that is equal to the number of the regions; and
a first processor for retrieving information from the first and the second memory, and calculating diffraction efficiencies of the entire diffraction lens using the formula                               E          jl                =                              ∑                          m              =              1                        M                    ⁢                                    W              m                        ⁢                          η              mjl                                                          (        5        )            
xe2x80x83wherein:
j: integer indicating the order of diffraction light
l: index of the wavelengths
Ejl: diffraction efficiency for j-th order diffraction light of the diffraction lens at the l-th wavelength
M: positive integer (M greater than 1) indicating the number of regions for which the diffraction efficiency is calculated
m: index of the region for which the diffraction efficiency is calculated
Wm: weight for the m-th region
xcex7mjl: diffraction efficiency for the j-th order diffraction light of the m-th region at the l-th wavelength
In accordance with the second configuration of the present invention, a method for calculating diffraction efficiencies of a diffraction lens divided into a plurality of regions, each region comprising at least one grating ring, the diffraction efficiencies corresponding to a plurality of wavelengths, comprises:
a first memory step of storing information about diffraction efficiencies of the regions at the plurality of wavelengths;
a second memory step of storing information about weights corresponding to the regions;
a third memory step of storing information about a relief cross-section shape of the diffraction lens;
a fourth memory step of storing information about the plurality of wavelengths;
a fifth memory step of storing information about refractive indices of a material of the diffraction lens at the wavelengths;
a fourth processing step of calculating a relief cross-section shape of the diffraction lens stored in the third memory step;
a second processing step of retrieving information stored in the third, fourth and fifth memory step, and calculating therefrom diffraction efficiencies of the regions at the plurality of wavelengths stored in the first memory step;
a third repeating step of repeating the second processing step for a number of times that is equal to the number of the wavelengths;
a fourth repeating step of repeating the third repeating step for a number of times that is equal to the number of the regions; and
a first processing step of retrieving information stored in the first and the second memory step, and calculating diffraction efficiencies of the entire diffraction lens using the formula                               E          jl                =                              ∑                          m              =              1                        M                    ⁢                                    W              m                        ⁢                          η              mjl                                                          (        5        )            
xe2x80x83wherein:
j: integer indicating the order of diffraction light
l: index of the wavelengths
Ejl: diffraction efficiency for j-th order diffraction light of the diffraction lens at the l-th wavelength
M: positive integer (M greater than 1) indicating the number of regions for which the diffraction efficiency is calculated
m: index of the region for which the diffraction efficiency is calculated
Wm: weight for the m-th region
xcex7mjl: diffraction efficiency for the j-th order diffraction light of the m-th region at the l-th wavelength.
In accordance with the second configuration of the present invention, a computer-readable recording medium stores a computer-executable program for calculating diffraction efficiencies of a diffraction lens divided into a plurality of regions, each region comprising at least one grating ring, the diffraction efficiencies corresponding to a plurality of wavelengths, wherein the program executes:
a first memory step of storing information about diffraction efficiencies of the regions at the plurality of wavelengths;
a second memory step of storing information about weights corresponding to the regions;
a third memory step of storing information about a relief cross-section shape of the diffraction lens;
a fourth memory step of storing information about the plurality of wavelengths;
a fifth memory step of storing information about refractive indices of a material of the diffraction lens at the wavelengths;
a fourth processing step of calculating a relief cross-section shape of the diffraction lens stored in the third memory step;
a second processing step of retrieving information stored in the third, fourth and fifth memory step, and calculating therefrom diffraction efficiencies of the regions at the plurality of wavelengths stored in the first memory step;
a third repeating step of repeating the second processing step for a number of times that is equal to the number of the wavelengths;
a fourth repeating step of repeating the third repeating step for a number of times that is equal to the number of the regions; and
a first processing step of retrieving information stored in the first and the second memory step, and calculating diffraction efficiencies of the entire diffraction lens using the formula                               E          jl                =                              ∑                          m              =              1                        M                    ⁢                                    W              m                        ⁢                          η              mjl                                                          (        5        )            
xe2x80x83wherein:
j: integer indicating the order of diffraction light
l: index of the wavelengths
Ejl: diffraction efficiency for j-th order diffraction light of the diffraction lens at the l-th wavelength
M: positive integer (M greater than 1) indicating the number of regions for which the diffraction efficiency is calculated
m: index of the region for which the diffraction efficiency is calculated
Wm: weight for the m-th region
xcex7mjl: diffraction efficiency for the j-th order diffraction light of the m-th region at the l-th wavelength.
In accordance with this second configuration of the present invention, the diffraction efficiencies at a plurality of wavelengths can be calculated with comparatively little memory and high speed.
According to the present invention, a lens-shape measurement apparatus for measuring the surface shape of a measurement object selected from the group consisting of a diffraction lens and a die for a diffraction lens comprises:
a shape measuring means for measuring the surface shape of the measurement object;
a processor device for substantially eliminating at least one of the macroscopic components selected from the group consisting of a spherical surface, an aspherical surface, and a plane from measurement data obtained with the shape measuring means; and
a device for calculating diffraction efficiencies of the diffraction lens based on the measured data from which the macroscopic component has been substantially eliminated;
wherein the device for calculating diffraction efficiencies is a device according to the first configuration of the present invention.
According to the present invention, a method for calculating diffraction efficiencies of a diffraction lens by measuring the surface shape of a measurement object selected from the group consisting of a diffraction lens and a die for a diffraction lens, comprises:
a shape measuring step of measuring the surface shape of the measurement object;
a processing step of substantially eliminating at least one of the macroscopic components selected from the group consisting of a spherical surface, an aspherical surface, and a plane from measurement data obtained in the shape measuring step; and
a step of calculating diffraction efficiencies of the diffraction lens based on the measured data from which the macroscopic component has been substantially eliminated;
wherein the step of calculating diffraction efficiencies is a method according to the first configuration of the present invention.
According to the present invention, a computer-readable recording medium stores a computer-executable program for calculating diffraction efficiencies of a diffraction lens by measuring the surface shape of a measurement object selected from the group consisting of a diffraction lens and a die for a diffraction lens, wherein the program executes:
a shape measuring step of measuring the surface shape of the measurement object;
a processing step of substantially eliminating at least one of the macroscopic components selected from the group consisting of a spherical surface, an aspherical surface, and a plane from measurement data obtained in the shape measuring step; and
a step of calculating diffraction efficiencies of the diffraction lens based on the measured data from which the macroscopic component has been substantially eliminated;
wherein the program for executing the step of calculating diffraction efficiencies is a program stored in a recording medium according to the first configuration of the present invention.
In accordance with this configuration, the diffraction efficiencies of diffraction lenses can be obtained by measuring relief profiles of actually obtained diffraction lenses or dies for molding diffraction lenses, so that it can be determined to what extent the precision of the obtained lens or the obtained die for molding lenses influences the diffraction efficiency. Thus, useful validation data for quality control such as precision tolerances or discrimination of faulty articles can be obtained. Moreover, by comparing diffraction efficiencies calculated from the actually obtained relief profile to diffraction efficiencies as determined from the design of a relief profile, the relation between the processing conditions for manufacturing a diffraction lens and the diffraction efficiency of the obtained lens can be determined. Consequently, this relation can be considered in the lens design, so that a precise prediction of the diffraction efficiency of the finally obtained diffraction lens and the selection of optimum manufacturing conditions become possible.
According to the present invention, an apparatus for designing diffraction lenses comprises:
an input for entering lens design data; and
a processor for calculating optical properties and diffraction efficiencies of the diffraction lens obtained on the basis of the design data;
wherein the processor for calculating the diffraction efficiencies is a device for calculating diffraction efficiencies according to the first configuration of the present invention.
According to the present invention, a method for designing diffraction lenses, comprises:
an input step of entering lens design data;
a processing step of calculating optical properties and diffraction efficiencies of the diffraction lens obtained on the basis of the design data;
an optimization step of optimizing the lens properties based on the result of the processing step;
wherein the processing step of calculating the diffraction efficiencies is a method for calculating diffraction efficiencies according to the first configuration of the present invention.
According to the present invention, a computer-readable recording medium stores a computer-executable program for designing a diffraction lens, and executing on a computer an evaluation function for evaluating lens properties; wherein the recording medium is in accordance with the first configuration of the present invention.
In accordance with this configuration, the optical properties and diffraction efficiencies of diffraction lenses obtained on the basis of design data can be predicted precisely, so that the lenses can be designed in consideration of restrictions due to both correction of chromatic aberration and tolerances of the diffraction efficiencies. Consequently, diffraction lenses with excellent characteristics can be designed in a short time and with high efficiency. Moreover, taking the conditions for the lens manufacturing process (for example the curvature radius of the tip of the cutting bit or the feed speed of the cutting bit) and their relation to the diffraction efficiency of the resulting lens into account, optimum manufacturing conditions can be determined at the time of lens design.
In accordance with the present invention, a combined refraction/diffraction lens comprises a refraction lens; and a diffraction lens comprising a plurality of concentric grating rings formed on at least one surface of the refraction lens; and satisfies the formula                               k          =                      f            ⁡                          (                                                1                                      f                    g                                                  +                                                      v                    g                                                                              f                      d                                        ⁢                                          v                      d                                                                                  )                                      ,                            (        6        )            
wherein:
f: total focal length of the combined refraction/diffraction lens
fd: focal length of the diffraction lens
fg: focal length of the refraction lens
xcexdd: partial dispersion coefficient at an applied wavelength region of the diffraction lens
xcexdg: partial dispersion coefficient at an applied wavelength region of the refraction lens
wherein k satisfies 0.1xe2x89xa6k.
In accordance with this configuration, combined refraction/diffraction lenses and dies for molding combined refraction/diffraction lenses, which are cut with a diamond bit, can be manufactured with high productivity.
In accordance with the present invention, a combined refraction/diffraction objective lens for use in an optical information recording/reproducing device comprises:
a single lens having an ingoing surface and an outgoing surface; and
a diffraction lens comprising a plurality of concentric grating rings formed on at least one surface of the single lens;
and satisfies the formula                               k          =                      f            ⁡                          (                                                1                                      f                    g                                                  +                                                      v                    g                                                                              f                      d                                        ⁢                                          v                      d                                                                                  )                                      ,                            (        6        )            
xe2x80x83wherein:
f: total focal length of the combined refraction/diffraction lens
fd: focal length of the diffraction lens
fg: focal length of the refraction lens
xcexdd: partial dispersion coefficient at an applied wavelength region of the diffraction lens
xcexdg: partial dispersion coefficient at an applied wavelength region of the refraction lens
xcexdg: partial dispersion coefficient at an applied wavelength region of the refraction lens
xe2x80x83wherein k satisfies 0.2xe2x89xa6kxe2x89xa60.6.
In accordance with this configuration, combined refraction/diffraction objective lenses and dies for molding combined refraction/diffraction objective lenses, which are cut with a diamond bit, can be manufactured with good chromatic aberration correction and high productivity. Consequently, an optical head including an objective lens according to the present invention can attain excellent signal output, because the focal length of the objective lens varies only little when the wavelength of the light source varies, and stray light can be reduced. Moreover, the optical heads comprising a single objective lens with such properties can be devised significantly smaller.
According to the present invention, a combined refraction/diffraction imaging lens comprises:
a single lens having an ingoing surface and an outgoing surface; and
a diffraction lens comprising a plurality of concentric grating rings formed on at least one surface of the single lens;
satisfying the formula                               k          =                      f            ⁡                          (                                                1                                      f                    g                                                  +                                                      v                    g                                                                              f                      d                                        ⁢                                          v                      d                                                                                  )                                      ,                            (        6        )            
xe2x80x83wherein:
f: total focal length of the combined refraction/diffraction lens
fd: focal length of the diffraction lens
fg: focal length of the refraction lens
xcexdd: partial dispersion coefficient at an applied wavelength region of the diffraction lens
xcexdg: partial dispersion coefficient at an applied wavelength region of the refraction lens
xcexdg: partial dispersion coefficient at an applied wavelength region of the refraction lens
xe2x80x83wherein k satisfies 0.3xe2x89xa6k.
In accordance with this configuration, imaging lenses and dies for molding imaging lenses, which are cut with a diamond bit, can be manufactured with high productivity. Moreover, if 0.4xe2x89xa6kxe2x89xa60.7, then processability is excellent, and an imaging lens with good resolution can be obtained. Consequently, an image pickup device comprising an imaging lens according to the present invention can attain a picture with little flare and excellent elimination of achromatic aberration.
Furthermore, in order to attain the above-mentioned objects, a lens with a grating element in accordance with the first configuration of the present invention is characterized by that, in the lens with a grating element in which chromatic aberration is corrected by forming concentric relief rings on a surface of the lens to provide diffractive effect, the pitch Pm of the relief rings satisfies the formula                                           P            m                     greater than                                                                       λ                  1                                ·                                  f                  d                                                            2                ⁢                m                                                    ,                            (        7        )            
where m is the ring number counted from the center of the lens, fd is the focal length of the grating element, and xcex1 is the principal wavelength of the grating element.
By satisfying Formula (7), a grating element surface can easily be produced. In addition, decrease in diffraction efficiency can be prevented, so that influence of unnecessary scattered light being projected on an image surface to decrease the imaging performance can be inhibited.
A lens with a grating element in accordance with the second configuration of the present invention is characterized by that, in the lens with a grating element in which chromatic aberration is corrected by forming concentric relief rings on a surface of the lens to provide diffractive effect, the itches of the relief rings gradually decrease to a certain position away from the optical axis, and gradually increase further away from the position.
By using such a configuration, the grating element surface can easily be produced, while function of excellent correction of chromatic aberration is maintained. Furthermore, decrease in diffraction efficiency can be prevented, so that influence of unnecessary scattered light being projected on an image surface to decrease the imaging performance can be inhibited.
A lens with a grating element in accordance with the third configuration of the present invention is characterized by that, in the lens with a grating element in which chromatic aberration is corrected by forming concentric relief rings on a surface of the lens to provide diffractive effect, the following Formula (8) is satisfied:                     0.2         less than                   "LeftBracketingBar"                      d            r                    "RightBracketingBar"                 less than         0.7                            (        8        )            
where r is the effective radius of the grating element surface, and d is the distance of the innermost ring of the relief from the optical axis.
By using such a configuration, a lens shape particularly useful for correcting lateral chromatic aberration can be obtained, and excessive correction of longitudinal chromatic aberration can also be inhibited.
Furthermore, in the lens with a grating element in accordance with the first to third configurations of the present invention, it is preferable that the grating element surface has a kinoform profile. Furthermore, it is preferable that the lens is made of glass or of plastic. By using such a structure, a lens with a grating element having a kinoform profile with excellent transcription performance can be achieved.
Furthermore, it is preferable that the lens with a grating element in accordance with the first to third configurations of the present invention is formed from an infrared absorbing material. By using such a material, influence of unnecessary light in the infrared spectrum generated by the grating element surface being projected on an image pickup device to decrease the imaging performance can be inhibited, so that good imaging performance can be maintained.
Furthermore, in forming an imaging apparatus, it is preferable that the imaging apparatus comprises a lens with a grating element in accordance with the first to third configurations of the present invention, an image pickup device and a signal processing circuit. By using such a structure, a small type imaging apparatus with very excellent imaging performance can be obtained.
Furthermore, in forming a reading apparatus, it is preferable that the reading apparatus comprises a lens having grating element in accordance with the first to third configurations of the present invention, an image sensor and a signal processing circuit. By using such a structure, a small type reading apparatus with very excellent imaging performance can be obtained.
In order to attain the above-mentioned objects, the present invention provides an optical system for reading image information or code information, which comprises a lens in which a grating element surface is formed on at least one surface of the lens. According to this structure, an optical system for reading with corrected chromatic aberration and having good imaging performance can be achieved.
Furthermore, it is preferable that the optical system for reading in accordance with the present invention can be moved on the optical axis by a driving device. According to this preferable example, manuscripts having different sizes can be read, and also an optical system for reading with corrected chromatic aberration and good imaging performance can be achieved.
Furthermore, in this preferable structure, it is preferable to satisfy
0.6 less than Yt/YW less than 1xe2x80x83xe2x80x83(14)
where YW is the maximum height of a manuscript when the optical system for reading is moved closest to the object side, and Yt is the maximum height of a manuscript when the optical system for reading is moved closest to the image side.
According to this preferable example, a small size optical system for reading having good imaging performance can be achieved.
Furthermore, in the optical system for reading in accordance with the present invention, it is preferable that the lens that constitutes the optical system for reading is only a single lens in which the grating element surface is formed, the image side surface of the lens being a convex surface and having a positive refractive power, and a diaphragm being placed on the object side from the lens. According to this preferable example, a low-priced optical system for reading with good imaging performance, in which chromatic aberration is corrected without increasing the number of the lens components, can be achieved.
Furthermore, in this preferable structure, it is preferable to satisfy
0.05 less than |r2/r1| less than 0.5,xe2x80x83xe2x80x83(9)
9 less than f/D less than 16,xe2x80x83xe2x80x83(10)
and
0.05 less than |f/fd| less than 0.15xe2x80x83xe2x80x83(11)
where r1 is the radius of curvature at the vertex of the object side surface of the lens, r2 is the radius of curvature at the vertex of the image side surface of the lens, D is the diameter of the diaphragm, f is the focal length of the entire optical system, and fd is the focal length of the grating element surface of the lens.
According to this preferable example, the following effects can be obtained. First, by satisfying Formula (9) above, an optimal lens shape in balance of various aberrations can be obtained. Then, by satisfying Formula (10) above, sufficient depth of field to prevent loss of image information or erroneous recognition of code information due to vibration etc. can be obtained. Then, by satisfying Formula (11) above, chromatic aberration can be excellently corrected.
In this case, it is further preferable that at least one surface of the lens is an aspheric surface with a local radius of curvature that becomes smaller with increasing distance from the optical axis. According to this preferable example, distortion aberration and curvature of field can be corrected effectively.
Furthermore, in the optical system for reading in accordance with the present invention, it is preferable to satisfy
450 nm less than xcex1 less than 600 nmxe2x80x83xe2x80x83(12)
where xcex1 is the principal wavelength when the grating element surface is formed.
According to this preferable example, unnecessary scattered light generated by the grating element surface can be prevented from being projected on an image sensor and decreasing the image performance.
Also, in this case, it is preferable that the grating element surface has a kinoform profile.
Furthermore, in the optical system for reading in accordance with the present invention, it is preferable that the lens having the grating element surface is made of glass or of plastic. According to this preferable example, a grating element surface having a kinoform profile with excellent transcription performance can be achieved.
In an optical system for reading in accordance with the present invention, it is preferable that the lens having the grating element surface is formed from an infrared absorbing material. According to this preferable example, particularly, unnecessary light in the infrared spectrum generated by the grating element surface can be prevented from being projected on an image sensor and decreasing the imaging performance, so that good imaging performance can be ensured.
Furthermore, in the optical system for reading in accordance with the present invention, it is preferable to satisfy
0.2 less than y/Y less than 0.6xe2x80x83xe2x80x83(13)
where Y is the maximum height of a manuscript and y is the maximum height of an image sensor.
According to this preferable example, miniaturization of the optical system for reading can be achieved.
Also, in this case, it is preferable that the meridional image surface has a better imaging performance than the sagittal image surface. According to this preferable example, precision of reading image information or code information can be enhanced, so that erroneous recognition can be prevented.
Furthermore, an imaging reading apparatus in accordance with the present invention comprises the optical system for reading in accordance with the present invention, an image sensor for converting the image information that is imaged by the optical system for reading into electric signals, and a circuit portion for processing the electric signals to process the image information. According to the structure of this image reading apparatus, the size of the entire image reading apparatus can be smaller than that of a conventional one, and also an image reading apparatus with good imaging performance can also be achieved.
Furthermore, a bar code reader in accordance with the present invention comprises the optical system for reading in accordance with the present invention, an image sensor for converting the bar code information that is imaged by the optical system for reading into electric signals, and a signal processing circuit having a circuit portion for decoding the bar code information. According to the structure of this bar code reader, the size of the entire bar code reader can be smaller than that of a conventional one, and a bar code reader with good imaging performance can also be achieved.